Caustic Formation in Tachyon Effective Field Theories

TL;DR

This paper investigates the dynamics of inhomogeneous tachyon fields in effective theories of unstable D-branes, revealing caustic formation as a potential artifact of derivative truncation, with better-behaved solutions in p-adic string models.

Contribution

It analytically compares tachyon dynamics across different effective actions and highlights the role of higher derivatives in avoiding caustics, proposing that caustics may be artifacts of truncated models.

Findings

Caustics form in all studied effective theories, indicating a possible pathology.

In p-adic string theory, solutions remain well-behaved without caustics.

Caustic formation may be due to derivative truncation, not fundamental physics.

Abstract

Certain configurations of D-branes, for example wrong dimensional branes or the brane-antibrane system, are unstable to decay. This instability is described by the appearance of a tachyonic mode in the spectrum of open strings ending on the brane(s). The decay of these unstable systems is described by the rolling of the tachyon field from the unstable maximum to the minimum of its potential. We analytically study the dynamics of the inhomogeneous tachyon field as it rolls towards the true vacuum of the theory in the context of several different tachyon effective actions. We find that the vacuum dynamics of these theories is remarkably similar and in particular we show that in all cases the tachyon field forms caustics where second and higher derivatives of the field blow up. The formation of caustics signals a pathology in the evolution since each of the effective actions considered is not reliable in the vicinity of a caustic. We speculate that the formation of caustics is an artifact of truncating the tachyon action, which should contain all orders of derivatives acting on the field, to a finite number of derivatives. Finally, we consider inhomogeneous solutions in p-adic string theory, a toy model of the bosonic tachyon which contains derivatives of all orders acting on the field. For a large class of initial conditions we conclusively show that the evolution is well behaved in this case. It is unclear if these caustics are a genuine prediction of string theory or not.